The
chemical-mechanical
relationship
of the
SiOC(H)
dielectric film
CadmusYuan, 0. vander Sluis,G.Q.Zhang,L. J.ErnstDepartmentof Precisionand MicrosystemEngineering,
Delft University ofTechnology, The Netherlands
W. D.vanDriel
NXPSemiconductors,IMO-BEInnovationBY1.055,The Netherlands
R. B. R. vanSilfhout
Philips AppliedTechnologies,HTC7, The Netherlands
B. J. Thijsse
StructureandChangeinMaterials,Departmentof Materials Science andEngineering, Delft University of Technol-ogy,The Netherlands
Abstract
We propose an atomic simulation techniques to
understand the chemical-mechanical relationship of amorphous/porous silica based low-dielectric (low-k) material (SiOC(H)). The mechanical stiffness of the
low-kmaterial isacritical issue for thereliabilityperformance of the IC backend structures. Due to the amorphous
nature of the low-k material which has tillnowunknown
molecular strucure, a novel algorithm is required to
generatethe molecularstructure. The moleculardynamics
(MD) mehtod is usedasthe simulation tool. Moreover, to
understand the variation of the mechanical stiffness and density by the chemicalconfiguration,sensitivity analyses have been performed. A fitting equation based on
homogenization theory is establishedtorepresentthe MD simulation results. The trends whichare indicatedby the simulation results exhibit good agreements with experiments from literature. Moreover, the simulation results indicate that the slight variation of the chemical configuration can induce significant change of the mechanical stiffness (over 80%)butnotthedensity.
1. Introduction
As feature sizes for the advanced IC continue to
shrink, the semiconductor industry is focusing the technologytominimize the intrinsic time delay for signal
propagation,
quantified by theresistance-capacitance (RC) delay. [1-2] The increasing demands for the electronic performance of the IC wiring have recently driven the replacement from aluminumtrace tocopper trace, and the alternative materials for SiO2 film with lower dielectricconstant [3]. Thesenewlow-k materials canbe classified by silsesquioxane based material, silica based material, organic polymers and amorphous carbon. In the silica based matrix material, the attempt to reduce the k value
can be obtained by two aspects. One can to replace
oxygen by the carbon, hydrogen (organosilicate glass,
OSG), or by fluorine (fluorinated silica glass, FSG). Generating the porosity within the material is another efficientapproach.
The silicon oxide based low-k materials (SiOC(H), also called black diamond, illustrated in Fig.
l(a))
arepreferred by industry because the fabricating processesof this materials exhibits high IC compatibility and high yielding rate. The k value can be reduced in two ways:
either chemically by replacing oxygen by the methyl
groups or H, OH, or physically by generating porosity
within the material [3]. The different Si atoms are
indicated with the usual denomination related to the number of0 atoms linkedto them: mono (M), di(D), tri (T) and quadri (Q) -functionalgroup. Theremaining links
are of the type Si-R, where R is the -CH3, 0 and OH
functional group [4]. In addition, when functional group
isreplaced by a silanol group, it is indicated withOH as
superscript. The Fig. lb illustrates thegroups of Q, T,D
andM. H3C\ 0 CH H,C-Si Si \1H 3o\H H,HC CH 0 C/ H-C3\0$ HC CSi CH 3 si.C H(a)H H CH H C Si cH3 Si\ 3\ IH3H'Si H SiiCH H3C Si Io H3C H- ' S 3 H3CIS' Si3 S-C HS H\ 0 Si H3C.iCH3 (a) -O-Si 0 Q -O-Si-CH3 0 TUblU
0o-
Si_
CH3 CH3 D 1°H3C-
Si CH3 CH3 M (b)Fig. 1 Illustration of the chemical structure of SiOC(H). (a) is the illustration of the material. (b) is the illustration of the connection capability of the basic buildingblocks
Among the materials of advanced IC backend
structures, the low-k material has low mechanical
stiffness, approximately 5-15 GPa. Experiments [4] show that enhancing the Young's modulus of the low-k material will increase the interfaceial toughness of SiOC(H)/TaN interface, which is known as the most
enhancement methods, the ultraviolet (UV) curing is
preferred because the SiOC(H) film can perform the
enhancement of the mechanical strength without much
loss of the dielectric characteristic. However, the
relationship between the chemical composition, porosity
and mechanical properties remained unclear, and a
trial-and-error design method is still common practice in the design/fabrication of the low-k material in the industry. Therefore, in this study, an atomic modeling method is developed, which is capableto analyze amorphous silica based material with porosity, to systematically study
relation between mechanical characteristics of the
SiOC(H) low-kfilmand it's chemicalstructure.
Theoretically, the amorphous nature of the SiOC(H)
filmtogether with the porosity increases the difficulty to
directly simulate its nano-scaled mechanical response.
Due tothe amorphousnature,the atomic structure canbe
hardly defined. The voidintheSiOC(H) molecule occurs
randomly, and the size of the void should be also carefully considerred. According the literature, the complicate molecule (like SiOC(H) film) canbe modeled when the accurate atomic structures and the potential functions are available. Yuan et al.[5-6] have stated that
one can model the long chain complicate dsDNA molecule and metal after theproperatomic structures and the potential functions are obtained, no matter using the analytical solution, finite element method or the moleculardynamics. Falk andLanger [7] haveapplied the
12-6 Lennard-Jones potential function to describe viscoplastic deformationinamorphous solids.
In this paper, an algorithm which is capable of
generating a reasonable molecular structure based onthe given concentration of basicbuilding blocks
(i.e.
Q, T, D,Mandvoid).Aseries of simulations will beperformedto
understand the sensitivity of the mechanical stiffness and density withrespectto the variation of the concentration ofbuilding blocks. Moreover, the fitting function based
on homogenization theory is applied to understand the mechanical behavior of SiOC(H). Two sets of experimental results, the SiOC(H) film before and after
UVcuring, areusedtovalidate the accuracyof the fitting function.
2. Theory
a.Moleculardynamics method
From the quantum mechanics point of view, matters
have dual natures: particle andwave. However, while the
geometryof the system is large enough, thewave nature
of individual components becomes un-apparent and the
system becomes determined. The molecular dynamics
(MD), which is widely used in IC technology, is a treatment for the many-particle problems, and a
determinedresponse is prescribed. This methodassumes
the atom(s) assolidspheres; theirmovementis described by coordinate variables. The interactions between the particles are described by the potential functions, also called force fields. When the wave nature of the particle will be ignored or considered implicitly by the potential
of the nano-scaled molecules. The following paragraphs will introduce the basic theory of MD, potential function,
time integration scheme, boundary/initial conditions and
limitation ofMD.
Theoretically, MD is based on the Newton's second
law of motion,
F =mina
(1)
for each particle i in a system constituted by N
particles. In Eq. (1), mi is the mass of particle i,
d= d2F Idt2is its acceleration, andF is the force acting on
the particle. Therefore, MD is a deterministic technique:
given an initial set of positions and velocities, the
subsequent time evolutioncanbe determined.
The interaction force between particles, which is
required in Eq. (1), can be defined by the potential
functions orforce fields:
Pi
=- U(r ,...,JN)ari (2)
where U is the potential function and
<k,k
=1...Nis theatomic coordinate.
b. Barloadingmethod
An atomistic method is established herein to predict
the mechanical stiffness parameter, which is represented
by the Young's modulus, of the nano-scaled structure.
The nano-scaled specimens are simulated by the MD
method withanadditionalenergyminimizationprocedure.
A bar model is established as illustrated in Fig. 2,
where one end of the bar is fixed and the oppositeend is
applied a displacement. The applied displacements and
reaction forces which obtainedatthe fixed endareusedto
extracttheYoung'smodulusbytheelasticity theory.Due
to the small deformation assumption ofelasticity [9], the total amount of the longitudinal deformation should be
less than 1.0% of the total length of the specimen.
More-over,basedon Saint-Venant's principle [9], amodel with
high aspect ratio (Llh) is required to prevent boundary effects, asillustrated inFig.2. Theloading andboundary
conditions areappliedatthelongitudinal direction. More-over, duetothe linearity assumptions,reaction force
out-puts are linear with the externally applied displacement.
The reaction forces Fi (i represent the i-th substeps) at
the fixed end) canbe extracted eitherbythe force of the
pseudo-springof the anchorpoint (illustratedinFig. 3)or
theenergygradientof the fixedatoms.
According to linear elasticity theory, the mechanical deformation of the uniaxially loaded barcanbe represent as: Ad=FL EA [9], where F , E , L andA represent
external mechanical force, Young's modulus, initial
length and initial cross
respectively. section area of the specimen,
L
F
d
Fig. 2. Illustration to bar loading model
dimensional, where each node has a maximum of 4
connection capabilities. As shown in Fig. 4a, the framework will define where the building block can or
can not be located. The building blocks (including the
void, Q, T, D and M) will randomly distribute into the framework (Fig. 4a) and the connection between blocks
will be established(Fig. 4b).However, most atomsshown inFig. 4a are not inthe equilibrium statebecause acubic framework is used. The geometrical optimization procedure [10] is used to minimize the atomic potential
energyof the connectioncatalogue.
CI
:onstrained atoma
/
'pseudo-spring
Non-constrained atom
Fig. 3 .Illustration scheme of the constraintedatoms
3. Atomistic Model ofSiOC(H)
The building blocks (Fig. lb), Q, T, D and M,
represent Si atoms having four, three, two and one
capabilitiesto connect toother basicblocks, respectively.
The size of the void is assumed to be the same as the
basic blocks, and no basic group can connect to this. In
the molecularmodeling of the SiOC(H) film, we further assumethatonlythesinglebond would exist betweenany
twobasic groups.Moreover, thecompositionof the low-k
film is assumedto follow the four basic blocks (Q, T, D
and M). Considering the basic building blocks with
silanol group and methyl group, like -OH of TOH and -CH3 ofT, both of them can not provide the connection
capabilitytothe other basicbuildingblocks andtheyhave the similar atomic mass. From the mechanical point of
view, the transferring of the force will be terminated at
the methyl or silanol group; therefore, the blocks with
methyl and silanol group will be mechanically similar.
Hence, the concentrations of the basic building blocks
with silanolgroup(e.g. TOHand DOH) aremergedinto the oneswithmethylgroups(e.g. T, D).
In practice, SiOC(H) films with thickness ranging
from 200to 700nmweredeposited by Chemical Vapour
Deposition (CVD)at350°C. TrimethylsilaneandO° were
used as precursorand gas for film deposition [4]. Due to
the similarityof the fabricationprocessbetween SiOC(H)
and SiO2, we assume that the connection catalogue of
SiOC(H) and SiO2 are similar. Therefore, these basic
blocks are assumed to be distributed onto a three
Fig. 4. Illustration of generating algorithm (a)
Two-dimensional illustration of the framework andlocatingof the basic building block. (b) Illustration to the obtained
topologyofamorphous SiOC(H)molecule
4. MDsimulation results and dataanalysis
4.1.MDsimulationparameters
In order to prevent boundary effects, the length and
cross section size of both cases are chosen as
approximately 10nm and 6.5 nm2 after the structural
relaxation; the number of basic building blocks is 1,224.
Both the casesofSiOC(H) molecule before and after UV
treatment are simulated by the commercial MD solver
Discover (version 2005.2) [10], and the force fields
between the atoms are described by COMPASS
(definition: cff9l, version 2.6) [10]. Both computations
areperformedon ani686 machine with 2.8GHz CPU and
CPU time for eachcaseisapproximately 270,500seconds.
In this paper, the canonical ensemble (NVT) ensemble,
which conserves the number ofatoms (N), the system
volume (V) and the temperature (T), is used. Moreover,
noperiodic boundary condition is appliedtoanymodel.
4.2. Parametric analysisonthecaseof before/after UV
treatment
Inordertoverifytheaccuracyof theproposed method,
two SiOC(H) models, Al (shown in Fig. 6) and A2,
having similar chemical composition as the SiOC(H)
before and after UV treatment, have been generated.
demonstrates the side view and cross sectional view of
model Al, where the dark yellow, red, grey and white
spheres represent, respectively, the silicon, oxygen,
carbon and hydrogenatom. The simulation results list at
thecaseAl and A2 of TableI. The simulation shows that
the Young's modulus and density of A2 (after UV
treatment) is slightly higher than Al (before UV
treatment), and the similar trend is also found in the experiment[4]. Notethat the simulateddensity is defined
as the ratio of atomic mass and molecule volume. Note
that the molecule volume is defined asthe volume which
is occupied by the molecular surface. This simple case
study demonstrates that the MD simulation has the capability to describe the variation ofYoung's modulus anddensityasfunction of chemicalcomposition.
(a)
Fig. 6. The molecular model Al.(a) side view, (b) cross
sectionview.
Considering the B series, the simulated Young's moduli and densities aresimilar because the concentration of basic building blocks are similar. The simulated
Young's moduli for the C series exhibit large variation,
but the density are similar. Therefore, the Young's
modulus is highly dependent upon the chemical composition but the density isnot.
TableIParametricanalysis of theSiOC(H)
Case Ratio of basicbuilding Young's Density
blocks modulus Q T D (GPa) (g/cm3) Al 16% 440o 29% 13.41 1.91 A2 21% 490o 19% 9.35 1.96 B1 21% 390o 29% 6.92 1.88 B2 31% 29% 29% 11.68 1.97 B3 15% 450o 16% 7.52 1.92 Cl 700o 25% 6.0%O 26.80 2.69 C2 22% 68% 9.4o 16.39 2.13 C3 11% 19% 69% 3.48 1.69
(b)
Fig. 5. (a) A generated approximate topology of SiOC(H) film.(b) the SiOC(H) filmafter minimization
4.3. Parametricanalysis
Three series ofparametric analyses are conducted as
listedinTable I: the chemical compositionintheBseries
are similartoAl andA2; the models C1, C2 andC3
em-phasize the effect ofQ, T andD, respectively; the D
se-ries comprises the extreme cases (e.g. SiO2 and air). The molecular modelgenerating method, geometrical size and loading/boundary conditions of the B and C series and model Dl follow the sameprocedure of models Al and
A2. The model Dl (SiO2) is established by the
conven-tional silicon oxide single lattice rather than theproposed generating algorithm, but the geometry and bound-ary/loading conditions of model Dl is the same as the other cases. For the model D2(air), both the Young's modulus and density ofD2 (air)are assumedaszero,and
nocomputational effort isrequired. The simulation results of thetest cases arelistedinTableI, and showninFig.7.
(a) (b)
4.3. Data management
In orderto understand how the concentration ofQ, T,
D and void impact theYoung's modulus and density, A
response function, fEd C +
C.
QrQ+ CTrT + CDrD +Cv,id v,id 1sused to obtain the sensitivity of the parametric analysis
For simplification, the ratio of M is merged into D
because the ratio ofMisrelatively small comparedtothe
rest. The coefficients of the response function are
normalized byc%,and the results areshowninFig. 8.The sensitivity shows that the basic building blocks of Q and
T will positively influence the Young's modulus and density. Increasing the porosity will decrease both
Young'smodulus anddensity. Varying the ratio ofDwill
notsignificantly influence the simulation result.
Moreover, a rather simple fitting function based on
homogenization theory is used to describe the numerical results. WedenoteYoung'smoduli and densities of100%
Q, T, D areEQ,ET,ED,
PQ,?PT
andPD, respectively. Hencetwo fitting functions for Young's modulus and density
canbe writtenas:
E=EQrQ+ETrT+EDrD
P=PQrQ+PTrT+PDrD
(3a) (3b) The coefficients can be obtained by the least square
method. Considering the detail experimental data on
(represented by the fitting equation) can not provide the
quantitative prediction for the SiOC(H) molecule.
However, MD can simulate the increasing trend of the
Young's modulus and density after the UV treatment
within acceptable accuracy. Thus, our work shows that
MDprovides atooltoperform material design, albeit ina
qualitative way. Note that the proposed simulation
procedure did not consider the complex fabrication
process but includes individual chemical concentration as
theinput. Void =D 100%- , .. Q 80%-60% 40%-20 0% Al A2 B1 B2 B3 C1 C2 C3 ° /// // t// // t// // '/1/'t//
301 Afte cmpetedbythee rt s
Fig. 7. The
density and
lowerpanel)
plots of concentration of basic blocks,
Young's modulus (from upper panel to
TableIIExperimental validationonpredicted trend
SiOC(H) BU* AU*
Concentration
47.4070o
21.700o
D 29.80% 20.50% E(GPa) 9.87 12.43 ByFitting function D(g/cm3) 1.99 2.02 E*** (GPa)
11±1
16±1
By Ex-periment D**** (g/CM3) 1.48 1.52*: BU and AU represent the SiOC(H) molecule before
and afterUVtreatment
: obtainedbynuclearmagneticresonance(NMR) :obtainedbynanoindentor
****: obtainedby X-ray reflectivity (XRR)
Sensitivity of Young's modulus
T D Void
I ,
-O- i-CH3'-O-Si-CH'
-O-S i-O° °l CH3 -FO-i-OH -O-Si-OH
?
> CH3, I/ /j/Arl A r X/Q
T D Void Sensitivityof DensityFig. 8.The sensitivity ofYoung'smodulus and density
Considering the magnitude of the Young's modulus
densitylisted in Table II, the values calculated by MD are
several times higher than the experimental results.
Possiblereasons are:
* No enough defect types are modeled, including dislocations andgrain boundaries;
* Size effect: due to the fact that the surface atom may not fulfill the requirement of the octet rule,
the surface atoms are often charged. This phenomenon can induce higher mechanical
stiffness. Note that the surface charge is consideredintheMDsimulation;
* Voidcollapse: the void presented inthe molecular topology might collapse by the structure
minimizationstep.After the minimizationstep,the
void will remain 1/3 to 1/4 compared to the original topology. Therefore, the porosity of the models is much smaller then theoneinreality.
However, asthe size of each model listedinTableI is
controlled and theporosity of SiOC(H) is approximately 10% inthe reality, the qualitative trend can be validated by the experimental results.
5. Conclusions
Aseries of molecularmodeling method is presentedto
simulate the amorphous low-k especially SiOC(H) material. The simulationprocedure comprises threesteps:
* generation of amorphous molecular model,
V/// IIIA K//
E,
_I
* parametric study by molecular dynamics (MD)
method and * data analysis.
Based on the chemical composition of the basic
building blocks (Q, T, D, M) and the void, the chemcial
topologies are obtained and the structural minimization
procedure is thenperformedto obtain the anapproximate
molecular structure. A series of parametric studies is
performed to understand the sensitivity of Young's
modulus and density while varying the chemical
concentration. Moreover, a simple fitting function based
on the homogenization theory is then applied to acquire
the Young's modulus and density as functions of
concentration of the basic building blocks. The experimental validation shows that theproposed method
can qualitatively represent the trend. Moreover, the simulation results indicate that the slight variation of the chemical configuration can induce significant change of the mechanical stiffness (over 80%) but notthe density.
However, inorderto achieve higherquantitative accuracy,
the molecular model should be improved by increasing the geometry size, inluding defects of realistic size and improve method for including theporosity.
Acknowledgments
The authors are grateful to Dr. F. lacopi for sharing her experimental results and experience of the low-k material. Also, the authors thank Dr. N. Iwamoto for valuable discussions on the simulation technique of molecular dynamics. C. Yuanthanks Dr. C. Menke and
Dr. J. Wescott for discussions on numerical simulation
technique.
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